

A322858


List of eperfect numbers that are not eunitary perfect.


3



17424, 87120, 121968, 226512, 296208, 331056, 400752, 505296, 540144, 609840, 644688, 714384, 749232, 818928, 923472, 1028016, 1062864, 1132560, 1167408, 1237104, 1271952, 1306800, 1376496, 1446192, 1481040, 1550736, 1585584, 1655280, 1690128, 1759824
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OFFSET

1,1


COMMENTS

The eunitary perfect numbers are numbers k such that the sum of their exponential unitary divisors (A322857) equals 2k. Apparently most of the eperfect numbers (A054979) are also eunitary perfect numbers: the first 150 eperfect numbers are also the first 150 eunitary perfect numbers. But A054979(151) = 17424 is not eunitary perfect.
Minculete and Tóth ask if there is any eunitary perfect number which is not eperfect.


LINKS



MATHEMATICA

f[p_, e_] := DivisorSum[e, p^# &]; esigma[n_] := Times @@ f @@@ FactorInteger[n]; ePerfectQ[n_] := esigma[n] == 2n; fu[p_, e_] := DivisorSum[e, p^# &, GCD[#, e/#]==1 &]; eusigma[n_] := Times @@ fu @@@ FactorInteger[n]; euPerfectQ[n_] := eusigma[n] == 2n; aQ[n_] := ePerfectQ[n] && !euPerfectQ[n]; Select[Range[125000], aQ]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



